I'm not so sure about that. Again, it's all in the execution and how it plays out but ATM it looks like Lorca still actively tries to be the 'better version of himself' he 'hoped to find' in the MU. We know, that MU Lorca was a captain of a starship of the Empire, meaning he probably has done morally questionable things by our standards, but something must have happened that challenged his point of view. He tried to assassinate the Emperor, somehow got into the PU afterwards and adapted pretty quickly to the rules and morals there. Not flawlessly, but he tried his best. There certainly is growth in there, if the writers want it that way, developing a new moral compass, getting 'better' and even though his attitude is still basically 'the end justifies the means' he softened relatively much compared to other MU versions we have seen so far.
Again, it depends on the writers intention and the execution, but there are, if they go that route, a lot of possibilities for growth and development into the UFP ideal somewhere in his future. And that's a very optimistic thing, that even someone like a MU captain can better himself, change and grow closer to the Picards and Janeways we are used to.
Yeah, but you're missing a crucial point: if Lorca is MU Lorca, then he has probably two or three episodes left. That's it. Done. We won't likely see the character again. There will be no further growth to show. Prime Universe Starfleet is not going to let MU Lorca serve as captain of anything, much less the Discovery. He would be too valuable an intelligence asset for Starfleet Intelligence to comb through (if not Section 31). What you are suggesting would presume that, assuming his identity becomes known, the bridge crew all collectively agree to "forget" his origins and how tenable is that?
Also, there's Adm Cornwell's threat so, even if the bridge crew did agree to "lie by omission," she might very well attempt to pull him from the centre seat.
Oh sure, the writers could hand wave all of that away, but it would stretch credulity to the breaking point A better explanation, particularly if you like Lorca, is that he's from Prime; he's simply less naïve than Picard.
To be honest, I don't think he's making it out of this story arc. If he is MU Lorca, he might be maneuvering for a second chance at the throne of the Terran Empire. In which case, he either succeeds or fails. Either way, he'll be written out.
Which really, really puts me in an uncomfortable position of having almost no reason to tune in week after week. Lorca and Tyler were/are my favourite characters. Stamets is fun but he cannot sustain the show. Everyone else...blech, meh, or you've-gotta-be-effin'-kidding-me.